Question

A cylinder of mass M and radius R is resting on a horizontal platform (which is parallel to the x-y plane) with its axis fixed along the y-axis and free to rotate about its axis. The platform is given a motion in the x-direction given by `x =A cos (omega t).` There is no slipping between the cylinder and platform. The maximum torque acting on the cylinder during its motion is ..................

Answer 1

`x=A cosomegat`
`implies(dx)/(dt)=-Aomegacosomegat`
`implies (d^(2)x)/(dt)=-Aomegacosomegat`
`:. |"max acceleration"|=Aomega^(2)`
`:. alpha_("max")=(Aomega^(2))/R`
Max torque`= Ialpha_("max")`
`=1/2MR^(2)xx(Aomega^(2))/R=1/2MRAomega^(2)`